*4.1.5 VECM estimation*

Having tested the existence of VECM, the analysis is to estimate on how shortterm and long-term relationships affect each other. The variables of FDR, NPF, and BOPO show the significant effect on lag 3 in monthly data.

**Table 6** shows the influence of each variable to other variables, particularly the relationship between FDR with NPF and FDR with BOPO. The short-term estimation results show that the FDR variable is influenced by the NPF variable in lag 1, which has a positive effect of 1.36%. In lag 2, the relationship of the NPF negatively affects FDR for 0.37%. Furthermore, in lag 3, the NPF has a positive effect to FDR with a value of 0.34%. Then, the FDR variable is influenced negatively by the BOPO in the first lag until the third.

**Table 6** shows the influence of BOPO and FDR to NPF. Results show that the NPF variable is influenced by the BOPO in the first lag which has a negative effect of 0.01% and the second lag also shows a negative effect of 0.02%. Then, the NPF variable is influenced by the BOPO in the third lag which has a positive effect that is 0.005%. Then, the NPF variable influenced by the FDR variable negatively affects the first lag until lag 3.

Furthermore, **Table 6** shows the relationship between BOPO with FDR and NPF. Empirically, BOPO is influenced positively by the FDR variable in the first and second lags for 0.12 and 0.11%, respectively, but in the third lag, the variables have a negative effect of 0.22%. On the contrary, the BOPO is influenced by the NPF, which has a negative effect on the first lag and third lag, which is 0.95 and 0.60%, respectively, but in the third lag, it shows a positive effect on the BOPO, namely, 1%.

**Table 7** shows the summary of direction among variables. Results generally indicate that NPF has positive effects toward FDR and BOPO. It implies that NPF that is a proxy variable for financing risk could trigger other risk occurrence, namely, liquidity and operational risks, in the short run.

Based on **Table 8**, VECM estimation analyzes the influence of variables in the long term. The FDR variable is influenced by NPF and BOPO variables. In the first lag, the FDR variable was influenced negatively by 72.58%. However, in contrast to the first lag, the FDR variable was influenced positively by BOPO for 9.02%. The NPF variable is influenced by the BOPO variable and the FDR variable. In the first lag, both variables negatively affect the values of 0.12 and 0.01%. The BOPO variables are influenced by FDR and NPF variables. In the first lag, the BOPO variable is


*4.1.6 Impulse response function (IRF)*

*Vector error correction model (VECM) in long term.*

*Source: Author's calculation.*

*Sources: Author's calculation.*

*Summary of direction of influence among variables.*

*Risk Analyses on Islamic Banks in Indonesia DOI: http://dx.doi.org/10.5772/intechopen.92245*

**Table 7.**

**Table 8.**

**63**

*4.1.6.1 Impulse response FDR to NPF*

and decreases toward equilibrium in the long run.

*4.1.6.2 Impulse response FDR to BOPO*

The IRF analysis explains the effects of shocks (shock) on one variable from the other variables, both in the short term and in the long term. The IRF also analyzes on how long the shocks take place. The horizontal axis shows the period of the year, while the vertical axis shows the response value in percentage, as the following details:

**Dependent variables Independent variables**

NPF Positive (lag-3) Not significant Negative (lag-2) FDR Positive (lag-1) Negative (lag-2) Negative (lags-1 and 2) BOPO Positive (lag 3) Negative (lag-3) Not significant

FDR NPF(1) 72.5889 [4.47911]

NPF BOPO 0.1244 [7.14765]

BOPO FDR 0.110746 [0.75713]

**NPF FDR BOPO**

**Variable Coefficient t-Static partial**

BOPO(1) 9.029681 [4.64308]

FDR 0.01378 [0.67799]

NPF 8.038916 [7.70009]

The first IRF analysis will explain the response received by the FDR to the *shock* of NPF. According to **Figure 3**, the response of the FDR if there was a shock from NPF is positive (+), where it shows an increase trend from periods 1 to 3. But, then in the 3rd to 10th period, the response of the FDR variable to NPF shock decreased. These results are consistent with findings from VECM estimation either in the short or long run where FDR will be fluctuating in short period and tends to be less volatile in the long run due to shocks from NPF. This condition indicates that liquidity risk in Islamic banks is only influenced by financing risk in the short run

**Figure 4** shows the response of FDR due to shocks coming from BOPO. Its responses are negative in the first three periods but tend to positive afterward. These conditions are consistent with VECM estimation where in the short run its relationship is negative, but positive in the long run. It indicates that liquidity risk is sensitive in both short and long runs due to shocks originated from operational risk.

*Sources: Author's calculation.*

#### **Table 6.** *VECM in short term.*

influenced by the FDR variable which has a positive effect of 0.01%. Then, in the first lag, the BOPO variable is influenced by the NPF variable, which has a negative effect of 8.03%. Therefore, in the long run, only operational risk—proxied by BOPO—affects positively the liquidity risk, proxied by FDR.


#### **Table 7.**

*Summary of direction of influence among variables.*


**Table 8.**

*Vector error correction model (VECM) in long term.*
